Introduction to Multiple Linear Regression
A statistical modelling technique to analyze and predict relationships between variables. Explore multiple linear regression with examples from social sciences. Discover practical examples like predicting income using socio-economic characteristics and estimating blood pressure based on factors like occupation, smoking, and age. Learn about the assumptions of MLR and how to deal with assumption violations by making adjustments to the model or data transformation when necessary.
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Multiple Linear Regression Mark Tranmer, Jen Murphy, Mark Elliot, Maria Pampaka Written by the authors. Narrated by AI voiceover. Full resource, see: Full resource, see: https://www.ncrm.ac.uk/resources/online/all/?id=20848
Introduction to Multiple Linear Regression A statistical modelling technique to analyse and predict relationships between variables. MLR helps understand the relationship between one dependent variable and two or more independent variables.
Overview Explore MLR with examples from social sciences. Downloadable worksheet and are also workbook available.
Foundations of MLR MLR builds on simple linear regression. It explores the effect of multiple independent variables on one dependent variable.
Simple Linear Regression Estimates the relationship between a response variable (y) and a single explanatory variable (x). Example: Predicting exam performance at age 16 based on exam results at age 11. Scatterplot of exam score at age 16, against score at age 11
Multiple Linear Regression Extends simple linear regression to include more explanatory variables. Still assumes the relationship between variables is linear.
Practical Examples Predict income using socio-economic characteristics. Estimate blood pressure considering factors like occupation, smoking, age, etc.
Assumptions of MLR The response variable is continuous. The relationship between variables is linear. Residuals are homoscedastic and normally distributed. Limited multicollinearity between variables. No extrinsic variables. Errors and observations should be independent. Homoscedastic residuals Heteroscedasticity:
Dealing with Assumption Violations If assumptions are violated, adjustments to the model or interpretation may be needed. In some cases, data transformation might be required.
